1. Field of the Invention
The present invention relates to an X-ray analysis apparatus, an X-ray analysis system, an X-ray analysis method, and an X-ray analysis program for converting an X-ray intensity distribution of discrete data determined for each pixel, from a first plane where the distribution is known into a second plane where the distribution is not known.
2. Description of the Related Art
While image data is usually two-dimensional, in consideration of an observation or measurement space, the image data can be regarded as data on a three-dimensional orthogonal coordinate system. Furthermore, data measured by a detector takes a discontinuous value for each pixel and is expressed as spatially discrete information as discrete data.
There is a case where such discrete data on an orthogonal coordinate system needs to be mapped to another coordinate system having the same or a lower dimension. Particularly in mapping in which data is expressed discretely in a mapping source and a mapping destination, one-to-one relationship can hold in a special conversion such as square pixel rotation in a multiple number of n/2. However, usually, one-to-one relationship does not hold between data elements even when the conversion operation is parallel transfer or rotation.
In the field of image processing, a method of approximately solving this problem exists for a long time and a nearest neighbor algorithm, a bilinear interpolation method, and a bicubic interpolation method are widely used. However, these methods do not guarantee preservation of a pixel value and an integral value thereof and are not always appropriately applied to an X-ray diffraction or scattering method in which a position and an integral value of a pixel value are important.
As a method of preserving a position and an integral value of a pixel value, there is proposed an approximation method of transforming a square pixel of a mapping source into a rectangular region in a mapping destination (refer to Non-patent Documents 1 to 4). However, in this method, while a pixel value is preserved, there is caused deformation of a high-frequency component of space frequency. Furthermore, a measurement value by a digital detector is limited to an integer, and sometimes an observation coordinate system does not coincide with an ideal observation coordinate system. For example, in the case such as the detector being inclined, data expression is treated only by using an integer value, and thus a rounding error to an integer value can be accumulated.